1. Field of the Invention
This invention relates to passive estimation of range from a sensor or seeker to an object and, more specifically, to a system and method for estimating such range based upon the change of size of the object with change of distance of the object of interest within a scene from the sensor.
2. Brief Description of the Prior Art
There are a number of situations wherein it is desirable to estimate the range to an object of interest or target. For example, if for some reason the ILS of an aircraft becomes disabled, it is highly advantageous to know the distance from the entrance to the runway to the aircraft to assist in landing. In the case of automotive travel, it would be highly desirable to always be aware of the distance between vehicles to avoid collisions. An air-to-air missile can use estimated range to the target to determine when to detonate its warhead. Anti-tank missiles which fly non-line-of-sight trajectories use range to determine target position on the battlefield.
Active techniques to measure range, such as radar, ladar and sonar, have been used extensively. The drawback of active ranging approaches, primarily in military applications, is that they can be easily detected by the target under attack. For example, if a submarine commander uses sonar to determine the position and velocity of an enemy ship, he runs a high risk of being detected. In such situations, it is advantageous to estimate range to the target passively.
The most common technique used to passively estimate range to a target employs a Kalman filter to estimate range from angle-only measurements. Initially, a rectangular Cartesian coordinate-based extended Kalman filter (EKF) is used to estimate target positions and velocities in Cartesian coordinates from angle measurements. Analytical and experimental work has shown that the Cartesian-based EKF suffers from instabilities and bias in the filter as discussed in "Fundamental Properties and Performance of Bearings-Only Target Motion Analysis", by S. C. Nardone et al., IEEE Transactions on Auto. Control, Vol. AC-29, No. 4, Sept. 1984, pp. 775-781. A paper entitled "An Angle-Only Tracking Filter in Modified Spherical Coordinates", by D. V. Stallard, AIAA Guidance, Navigation, & Control Conference, Vol. 1, Aug. 17-19, 1987, pp. 542-550 describes the use of modified spherical coordinates (MSC) which reduces problems with EKF observability, range bias and covariance ill-conditioning. In this paper, line-of-sight (LOS) angles of a missile are used as both filter measurements and states. This paper proposed the following six-state vector: EQU x=.THETA..THETA..PSI..omega.1/rr/r!.sup.T
where .THETA. is the pitch LOS angle, .THETA.=d.THETA./dt, .PSI. T is the yaw LOS angle, .omega.=(d.PSI./dt) cos .THETA., r is range to the target along the LOS and r is the range-rate to the target along the LOS. An important point that is noted is that the 1/r state can be determined only if the missile accelerates in a direction perpendicular to the LOS because, as can be demonstrated mathematically, when 1/r becomes observable, range can be passively estimated.
Considering a command to LOS flight from a gunner to a target, the missile flies as closely as possible to the LOS of the gunner. Missile accelerations perpendicular to the LOS due to climbing, diving or yaw maneuvers are undesirable since such maneuvers may cause the missile to hit the ground or miss the target completely. However, since the angle-only measurement EKF approaches require maneuvers away from the LOS, these techniques cannot be used for LOS-only engagements.